I just recently started snowboarding and only went up 3 times on a cheap gear.
I'm 18 year old male, 6' 2" with a size 14 foot, and weigh around 185-190 lbs. I bought a 164cm Burton board with K2 bindings. I set the angles at 15/-15.

The problem I seem to have is a lot of pressure on my back foot. When I'm going down I put most of my weight on my back foot and it really starts to sore in my quad. And it caused me to stop and take breaks to rest my foot.

So the question is where lies the problem? Is the problem in my set up or the way I ride?

P.S. Also I forgot to mention that my snowboard is not wide even though it should be for my foot size.

When I started I was often tired out too. That will change as you improve your technique. Try practicing lots of S turns to get smoother. It helps to think about the edges of your board when riding to get an understanding of how you are turning and how you can work with the board instead of thrashing muscles working against it.

Try setting the back binding to 0 or even plus 1 -5, this will help with turning more efficiently at first. Switch and crazy duck settings can come later.

Also, if you haven't already, get up to the blue/red steeper runs as thinking about edge hold easier to concieve with a bit of gradient.

Hey rkudryashov, muscle fatigue is a common thing in new riders, mainly because your legs have yet to get used to the strain which normally wouldn't occur.
The burn is caused by your quad's acting as shock absorbers for your riding.

One thing you could possibly do is to adjust your back binding to a more negative setting, which can ease the pressure.

When you're walking on the side of the road your body is perpendicular to the ground and you have full control of your movements
When you're riding down a hill it's the same principle, your body has to be perpendicular to the ground to maintain control

You should be initiating your turns with your front foot and it'll feel like you're leaning down the hill when you're actually just squaring up to the surface you're riding.
Snowolf has a very good explanation on the specifics of how this is done.